Binning With Tree

1 Load Data

import polars as pl
import plotly.express as px

import plotly.io as pio
import matplotlib.pyplot as plt

pio.renderers.default = "notebook"

%config InlineBackend.figure_format = 'retina'

2 Data Preparation

df = pl.read_csv("data/credit.csv.gz")

layout_config = dict(
    width=800,
    height=500,
    template="simple_white",
    plot_bgcolor="white",
    paper_bgcolor="white",
    # xaxis=dict(
    #     showline=True,
    #     linewidth=1,
    #     linecolor="black",
    #     mirror=True,
    #     showgrid=True,
    # ),
    # yaxis=dict(
    #     showline=True,
    #     linewidth=1,
    #     linecolor="black",
    #     mirror=True,
    #     showgrid=True,
    # ),
)

fig = df.pipe(px.histogram, x="limit_bal", nbins=40, color="y", histnorm="density")
fig.update_layout(
    title=dict(text="Distribution of Balance", x=0.5, xanchor="center"), **layout_config
)
fig.update_layout(bargap=0.3, xaxis_tickformat=",d")
fig.show()

How to evaluate the performance of the binning?

3 Binning and Credit Modelling

Binning is required to for WOE transformation, IV and PSI calculation. It has many advantages - Robustness (against outliers)

from sklearn.model_selection import train_test_split

df_train, df_valid = train_test_split(df, test_size=0.5, random_state=42)

3.1 Calculate WOE using QCUT

More or less bins? - More bins - Less information lost, less bias - Less bins - More stable

The easiest cut is qcut

def calculate_woe(df, x, y):
    df_woe = (
        df.group_by(x)
        .agg(
            pl.len().alias("obs"),
            pl.col(y).eq(0).sum().alias("y=0"),
            pl.col(y).sum().alias("y=1"),
        )
        .with_columns(
            (pl.col("y=0", "y=1") / pl.col("y=0", "y=1").sum()).name.suffix("_rate"),
        )
        .with_columns(
            (pl.col("y=1_rate") / pl.col("y=0_rate")).log().alias("woe"),
        )
        .with_columns(
            (pl.col("y=1_rate") - pl.col("y=0_rate")).mul(pl.col("woe")).alias("iv")
        )
        .pipe(lambda x: x.sort(x.columns[0]))
    )

    return df_woe

5 Bins

from plotly import graph_objects as go
from plotly.subplots import make_subplots

subplot_titles = [
    "WoE(5 bins)",
    "WoE(10 bins)",
    "WoE(20 bins)",
    "Obs(5 bins)",
    "Obs(10 bins)",
    "Obs(20 bins)",
]

fig = make_subplots(
    rows=2,
    cols=3,
    subplot_titles=subplot_titles,
    horizontal_spacing=0.05,
    vertical_spacing=0.15,
    shared_yaxes=True,
    shared_xaxes=True,
)

for i, n_bins in enumerate([5, 10, 20], start=1):
    df_woe_limit_bal = df_train.pipe(
        calculate_woe,
        pl.col("limit_bal").truediv(1_000).qcut(n_bins, allow_duplicates=True),
        "y",
    )

    fig.add_trace(
        go.Scatter(
            mode="lines+markers",
            x=df_woe_limit_bal["limit_bal"],
            y=df_woe_limit_bal["woe"],
            name=f"WoE({n_bins} bins)",
        ),
        row=1,
        col=i,
    )

    # Observation count plots in second row
    fig.add_trace(
        go.Bar(
            x=df_woe_limit_bal["limit_bal"],
            y=df_woe_limit_bal["obs"],
            name=f"Obs({n_bins} bins)",
            opacity=0.5,
        ),
        row=2,
        col=i,
    )

fig.update_layout(
    template="simple_white",
    height=500,
    width=900,
    showlegend=False,
    title=dict(
        text="WoE and Observation Counts with different number of bins",
        x=0.5,
        xanchor="center",
    ),
)

fig.update_xaxes(tickangle=90)


fig.show()

Bias-variance trade off

More bins - Less bias - More variance - Less monotonic - Less stable (PSI)

def get_qcut_breaks(series: pl.Series, q: int = 5):
    s = (
        df_train["limit_bal"]
        .qcut(q, allow_duplicates=True, include_breaks=True)
        .struct.field("breakpoint")
        .unique()
    )

    breaks = s.filter(~s.is_infinite()).sort(descending=False).to_list()
    return breaks

def calculate_psi(expected: pl.Series, actual: pl.Series) -> float:

    expected_dist = expected.rename("x").value_counts().rename({"count": "count_exp"})
    actual_dist = actual.rename("x").value_counts().rename({"count": "count_act"})

    psi = (
        expected_dist.join(actual_dist, on="x", how="full", coalesce=True)
        .with_columns(
            (pl.col("count_exp") / pl.col("count_exp").sum())
            .fill_null(0.0001)
            .alias("pct_exp"),
            (pl.col("count_act") / pl.col("count_act").sum())
            .fill_null(0.0001)
            .alias("pct_act"),
        )
        .with_columns(
            psi=(
                (pl.col("pct_act") - pl.col("pct_exp"))
                * (pl.col("pct_act") / pl.col("pct_exp")).log()
            )
        )
    )

    return psi

breaks = get_qcut_breaks(df_train["limit_bal"], q=10)

result = []
for q in range(2, 30):
    breaks = get_qcut_breaks(df_train["limit_bal"], q=q)
    iv = calculate_woe(df_train, pl.col("limit_bal").cut(breaks), "y")
    psi = calculate_psi(
        df_train["limit_bal"].cut(breaks), df_valid["limit_bal"].cut(breaks)
    )
    result.append(dict(q=q, iv=iv["iv"].sum(), psi=psi["psi"].sum()))

pl.DataFrame(result).head(10)

shape: (10, 3)

q	iv	psi
i64	f64	f64
2	0.12329	0.000028
3	0.138538	0.00007
4	0.162616	0.000181
5	0.156567	0.00018
6	0.164844	0.000429
7	0.165888	0.00086
8	0.17931	0.000432
9	0.182535	0.000539
10	0.186456	0.000293
11	0.184024	0.000561

from sklearn.tree import DecisionTreeClassifier, plot_tree

DecisionTreeClassifier?

Init signature:
DecisionTreeClassifier(
    *,
    criterion='gini',
    splitter='best',
    max_depth=None,
    min_samples_split=2,
    min_samples_leaf=1,
    min_weight_fraction_leaf=0.0,
    max_features=None,
    random_state=None,
    max_leaf_nodes=None,
    min_impurity_decrease=0.0,
    class_weight=None,
    ccp_alpha=0.0,
    monotonic_cst=None,
)
Docstring:     
A decision tree classifier.

Read more in the :ref:`User Guide <tree>`.

Parameters
----------
criterion : {"gini", "entropy", "log_loss"}, default="gini"
    The function to measure the quality of a split. Supported criteria are
    "gini" for the Gini impurity and "log_loss" and "entropy" both for the
    Shannon information gain, see :ref:`tree_mathematical_formulation`.

splitter : {"best", "random"}, default="best"
    The strategy used to choose the split at each node. Supported
    strategies are "best" to choose the best split and "random" to choose
    the best random split.

max_depth : int, default=None
    The maximum depth of the tree. If None, then nodes are expanded until
    all leaves are pure or until all leaves contain less than
    min_samples_split samples.

min_samples_split : int or float, default=2
    The minimum number of samples required to split an internal node:

    - If int, then consider `min_samples_split` as the minimum number.
    - If float, then `min_samples_split` is a fraction and
      `ceil(min_samples_split * n_samples)` are the minimum
      number of samples for each split.

    .. versionchanged:: 0.18
       Added float values for fractions.

min_samples_leaf : int or float, default=1
    The minimum number of samples required to be at a leaf node.
    A split point at any depth will only be considered if it leaves at
    least ``min_samples_leaf`` training samples in each of the left and
    right branches.  This may have the effect of smoothing the model,
    especially in regression.

    - If int, then consider `min_samples_leaf` as the minimum number.
    - If float, then `min_samples_leaf` is a fraction and
      `ceil(min_samples_leaf * n_samples)` are the minimum
      number of samples for each node.

    .. versionchanged:: 0.18
       Added float values for fractions.

min_weight_fraction_leaf : float, default=0.0
    The minimum weighted fraction of the sum total of weights (of all
    the input samples) required to be at a leaf node. Samples have
    equal weight when sample_weight is not provided.

max_features : int, float or {"sqrt", "log2"}, default=None
    The number of features to consider when looking for the best split:

        - If int, then consider `max_features` features at each split.
        - If float, then `max_features` is a fraction and
          `max(1, int(max_features * n_features_in_))` features are considered at
          each split.
        - If "sqrt", then `max_features=sqrt(n_features)`.
        - If "log2", then `max_features=log2(n_features)`.
        - If None, then `max_features=n_features`.

    Note: the search for a split does not stop until at least one
    valid partition of the node samples is found, even if it requires to
    effectively inspect more than ``max_features`` features.

random_state : int, RandomState instance or None, default=None
    Controls the randomness of the estimator. The features are always
    randomly permuted at each split, even if ``splitter`` is set to
    ``"best"``. When ``max_features < n_features``, the algorithm will
    select ``max_features`` at random at each split before finding the best
    split among them. But the best found split may vary across different
    runs, even if ``max_features=n_features``. That is the case, if the
    improvement of the criterion is identical for several splits and one
    split has to be selected at random. To obtain a deterministic behaviour
    during fitting, ``random_state`` has to be fixed to an integer.
    See :term:`Glossary <random_state>` for details.

max_leaf_nodes : int, default=None
    Grow a tree with ``max_leaf_nodes`` in best-first fashion.
    Best nodes are defined as relative reduction in impurity.
    If None then unlimited number of leaf nodes.

min_impurity_decrease : float, default=0.0
    A node will be split if this split induces a decrease of the impurity
    greater than or equal to this value.

    The weighted impurity decrease equation is the following::

        N_t / N * (impurity - N_t_R / N_t * right_impurity
                            - N_t_L / N_t * left_impurity)

    where ``N`` is the total number of samples, ``N_t`` is the number of
    samples at the current node, ``N_t_L`` is the number of samples in the
    left child, and ``N_t_R`` is the number of samples in the right child.

    ``N``, ``N_t``, ``N_t_R`` and ``N_t_L`` all refer to the weighted sum,
    if ``sample_weight`` is passed.

    .. versionadded:: 0.19

class_weight : dict, list of dict or "balanced", default=None
    Weights associated with classes in the form ``{class_label: weight}``.
    If None, all classes are supposed to have weight one. For
    multi-output problems, a list of dicts can be provided in the same
    order as the columns of y.

    Note that for multioutput (including multilabel) weights should be
    defined for each class of every column in its own dict. For example,
    for four-class multilabel classification weights should be
    [{0: 1, 1: 1}, {0: 1, 1: 5}, {0: 1, 1: 1}, {0: 1, 1: 1}] instead of
    [{1:1}, {2:5}, {3:1}, {4:1}].

    The "balanced" mode uses the values of y to automatically adjust
    weights inversely proportional to class frequencies in the input data
    as ``n_samples / (n_classes * np.bincount(y))``

    For multi-output, the weights of each column of y will be multiplied.

    Note that these weights will be multiplied with sample_weight (passed
    through the fit method) if sample_weight is specified.

ccp_alpha : non-negative float, default=0.0
    Complexity parameter used for Minimal Cost-Complexity Pruning. The
    subtree with the largest cost complexity that is smaller than
    ``ccp_alpha`` will be chosen. By default, no pruning is performed. See
    :ref:`minimal_cost_complexity_pruning` for details.

    .. versionadded:: 0.22

monotonic_cst : array-like of int of shape (n_features), default=None
    Indicates the monotonicity constraint to enforce on each feature.
      - 1: monotonic increase
      - 0: no constraint
      - -1: monotonic decrease

    If monotonic_cst is None, no constraints are applied.

    Monotonicity constraints are not supported for:
      - multiclass classifications (i.e. when `n_classes > 2`),
      - multioutput classifications (i.e. when `n_outputs_ > 1`),
      - classifications trained on data with missing values.

    The constraints hold over the probability of the positive class.

    Read more in the :ref:`User Guide <monotonic_cst_gbdt>`.

    .. versionadded:: 1.4

Attributes
----------
classes_ : ndarray of shape (n_classes,) or list of ndarray
    The classes labels (single output problem),
    or a list of arrays of class labels (multi-output problem).

feature_importances_ : ndarray of shape (n_features,)
    The impurity-based feature importances.
    The higher, the more important the feature.
    The importance of a feature is computed as the (normalized)
    total reduction of the criterion brought by that feature.  It is also
    known as the Gini importance [4]_.

    Warning: impurity-based feature importances can be misleading for
    high cardinality features (many unique values). See
    :func:`sklearn.inspection.permutation_importance` as an alternative.

max_features_ : int
    The inferred value of max_features.

n_classes_ : int or list of int
    The number of classes (for single output problems),
    or a list containing the number of classes for each
    output (for multi-output problems).

n_features_in_ : int
    Number of features seen during :term:`fit`.

    .. versionadded:: 0.24

feature_names_in_ : ndarray of shape (`n_features_in_`,)
    Names of features seen during :term:`fit`. Defined only when `X`
    has feature names that are all strings.

    .. versionadded:: 1.0

n_outputs_ : int
    The number of outputs when ``fit`` is performed.

tree_ : Tree instance
    The underlying Tree object. Please refer to
    ``help(sklearn.tree._tree.Tree)`` for attributes of Tree object and
    :ref:`sphx_glr_auto_examples_tree_plot_unveil_tree_structure.py`
    for basic usage of these attributes.

See Also
--------
DecisionTreeRegressor : A decision tree regressor.

Notes
-----
The default values for the parameters controlling the size of the trees
(e.g. ``max_depth``, ``min_samples_leaf``, etc.) lead to fully grown and
unpruned trees which can potentially be very large on some data sets. To
reduce memory consumption, the complexity and size of the trees should be
controlled by setting those parameter values.

The :meth:`predict` method operates using the :func:`numpy.argmax`
function on the outputs of :meth:`predict_proba`. This means that in
case the highest predicted probabilities are tied, the classifier will
predict the tied class with the lowest index in :term:`classes_`.

References
----------

.. [1] https://en.wikipedia.org/wiki/Decision_tree_learning

.. [2] L. Breiman, J. Friedman, R. Olshen, and C. Stone, "Classification
       and Regression Trees", Wadsworth, Belmont, CA, 1984.

.. [3] T. Hastie, R. Tibshirani and J. Friedman. "Elements of Statistical
       Learning", Springer, 2009.

.. [4] L. Breiman, and A. Cutler, "Random Forests",
       https://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm

Examples
--------
>>> from sklearn.datasets import load_iris
>>> from sklearn.model_selection import cross_val_score
>>> from sklearn.tree import DecisionTreeClassifier
>>> clf = DecisionTreeClassifier(random_state=0)
>>> iris = load_iris()
>>> cross_val_score(clf, iris.data, iris.target, cv=10)
...                             # doctest: +SKIP
...
array([ 1.     ,  0.93...,  0.86...,  0.93...,  0.93...,
        0.93...,  0.93...,  1.     ,  0.93...,  1.      ])
File:           ~/.pyenv/versions/3.10.13/lib/python3.10/site-packages/sklearn/tree/_classes.py
Type:           ABCMeta
Subclasses:     ExtraTreeClassifier

min_impurity_decrease

DecisionTreeClassifier?

Init signature:
DecisionTreeClassifier(
    *,
    criterion='gini',
    splitter='best',
    max_depth=None,
    min_samples_split=2,
    min_samples_leaf=1,
    min_weight_fraction_leaf=0.0,
    max_features=None,
    random_state=None,
    max_leaf_nodes=None,
    min_impurity_decrease=0.0,
    class_weight=None,
    ccp_alpha=0.0,
    monotonic_cst=None,
)
Docstring:     
A decision tree classifier.

Read more in the :ref:`User Guide <tree>`.

Parameters
----------
criterion : {"gini", "entropy", "log_loss"}, default="gini"
    The function to measure the quality of a split. Supported criteria are
    "gini" for the Gini impurity and "log_loss" and "entropy" both for the
    Shannon information gain, see :ref:`tree_mathematical_formulation`.

splitter : {"best", "random"}, default="best"
    The strategy used to choose the split at each node. Supported
    strategies are "best" to choose the best split and "random" to choose
    the best random split.

max_depth : int, default=None
    The maximum depth of the tree. If None, then nodes are expanded until
    all leaves are pure or until all leaves contain less than
    min_samples_split samples.

min_samples_split : int or float, default=2
    The minimum number of samples required to split an internal node:

    - If int, then consider `min_samples_split` as the minimum number.
    - If float, then `min_samples_split` is a fraction and
      `ceil(min_samples_split * n_samples)` are the minimum
      number of samples for each split.

    .. versionchanged:: 0.18
       Added float values for fractions.

min_samples_leaf : int or float, default=1
    The minimum number of samples required to be at a leaf node.
    A split point at any depth will only be considered if it leaves at
    least ``min_samples_leaf`` training samples in each of the left and
    right branches.  This may have the effect of smoothing the model,
    especially in regression.

    - If int, then consider `min_samples_leaf` as the minimum number.
    - If float, then `min_samples_leaf` is a fraction and
      `ceil(min_samples_leaf * n_samples)` are the minimum
      number of samples for each node.

    .. versionchanged:: 0.18
       Added float values for fractions.

min_weight_fraction_leaf : float, default=0.0
    The minimum weighted fraction of the sum total of weights (of all
    the input samples) required to be at a leaf node. Samples have
    equal weight when sample_weight is not provided.

max_features : int, float or {"sqrt", "log2"}, default=None
    The number of features to consider when looking for the best split:

        - If int, then consider `max_features` features at each split.
        - If float, then `max_features` is a fraction and
          `max(1, int(max_features * n_features_in_))` features are considered at
          each split.
        - If "sqrt", then `max_features=sqrt(n_features)`.
        - If "log2", then `max_features=log2(n_features)`.
        - If None, then `max_features=n_features`.

    Note: the search for a split does not stop until at least one
    valid partition of the node samples is found, even if it requires to
    effectively inspect more than ``max_features`` features.

random_state : int, RandomState instance or None, default=None
    Controls the randomness of the estimator. The features are always
    randomly permuted at each split, even if ``splitter`` is set to
    ``"best"``. When ``max_features < n_features``, the algorithm will
    select ``max_features`` at random at each split before finding the best
    split among them. But the best found split may vary across different
    runs, even if ``max_features=n_features``. That is the case, if the
    improvement of the criterion is identical for several splits and one
    split has to be selected at random. To obtain a deterministic behaviour
    during fitting, ``random_state`` has to be fixed to an integer.
    See :term:`Glossary <random_state>` for details.

max_leaf_nodes : int, default=None
    Grow a tree with ``max_leaf_nodes`` in best-first fashion.
    Best nodes are defined as relative reduction in impurity.
    If None then unlimited number of leaf nodes.

min_impurity_decrease : float, default=0.0
    A node will be split if this split induces a decrease of the impurity
    greater than or equal to this value.

    The weighted impurity decrease equation is the following::

        N_t / N * (impurity - N_t_R / N_t * right_impurity
                            - N_t_L / N_t * left_impurity)

    where ``N`` is the total number of samples, ``N_t`` is the number of
    samples at the current node, ``N_t_L`` is the number of samples in the
    left child, and ``N_t_R`` is the number of samples in the right child.

    ``N``, ``N_t``, ``N_t_R`` and ``N_t_L`` all refer to the weighted sum,
    if ``sample_weight`` is passed.

    .. versionadded:: 0.19

class_weight : dict, list of dict or "balanced", default=None
    Weights associated with classes in the form ``{class_label: weight}``.
    If None, all classes are supposed to have weight one. For
    multi-output problems, a list of dicts can be provided in the same
    order as the columns of y.

    Note that for multioutput (including multilabel) weights should be
    defined for each class of every column in its own dict. For example,
    for four-class multilabel classification weights should be
    [{0: 1, 1: 1}, {0: 1, 1: 5}, {0: 1, 1: 1}, {0: 1, 1: 1}] instead of
    [{1:1}, {2:5}, {3:1}, {4:1}].

    The "balanced" mode uses the values of y to automatically adjust
    weights inversely proportional to class frequencies in the input data
    as ``n_samples / (n_classes * np.bincount(y))``

    For multi-output, the weights of each column of y will be multiplied.

    Note that these weights will be multiplied with sample_weight (passed
    through the fit method) if sample_weight is specified.

ccp_alpha : non-negative float, default=0.0
    Complexity parameter used for Minimal Cost-Complexity Pruning. The
    subtree with the largest cost complexity that is smaller than
    ``ccp_alpha`` will be chosen. By default, no pruning is performed. See
    :ref:`minimal_cost_complexity_pruning` for details.

    .. versionadded:: 0.22

monotonic_cst : array-like of int of shape (n_features), default=None
    Indicates the monotonicity constraint to enforce on each feature.
      - 1: monotonic increase
      - 0: no constraint
      - -1: monotonic decrease

    If monotonic_cst is None, no constraints are applied.

    Monotonicity constraints are not supported for:
      - multiclass classifications (i.e. when `n_classes > 2`),
      - multioutput classifications (i.e. when `n_outputs_ > 1`),
      - classifications trained on data with missing values.

    The constraints hold over the probability of the positive class.

    Read more in the :ref:`User Guide <monotonic_cst_gbdt>`.

    .. versionadded:: 1.4

Attributes
----------
classes_ : ndarray of shape (n_classes,) or list of ndarray
    The classes labels (single output problem),
    or a list of arrays of class labels (multi-output problem).

feature_importances_ : ndarray of shape (n_features,)
    The impurity-based feature importances.
    The higher, the more important the feature.
    The importance of a feature is computed as the (normalized)
    total reduction of the criterion brought by that feature.  It is also
    known as the Gini importance [4]_.

    Warning: impurity-based feature importances can be misleading for
    high cardinality features (many unique values). See
    :func:`sklearn.inspection.permutation_importance` as an alternative.

max_features_ : int
    The inferred value of max_features.

n_classes_ : int or list of int
    The number of classes (for single output problems),
    or a list containing the number of classes for each
    output (for multi-output problems).

n_features_in_ : int
    Number of features seen during :term:`fit`.

    .. versionadded:: 0.24

feature_names_in_ : ndarray of shape (`n_features_in_`,)
    Names of features seen during :term:`fit`. Defined only when `X`
    has feature names that are all strings.

    .. versionadded:: 1.0

n_outputs_ : int
    The number of outputs when ``fit`` is performed.

tree_ : Tree instance
    The underlying Tree object. Please refer to
    ``help(sklearn.tree._tree.Tree)`` for attributes of Tree object and
    :ref:`sphx_glr_auto_examples_tree_plot_unveil_tree_structure.py`
    for basic usage of these attributes.

See Also
--------
DecisionTreeRegressor : A decision tree regressor.

Notes
-----
The default values for the parameters controlling the size of the trees
(e.g. ``max_depth``, ``min_samples_leaf``, etc.) lead to fully grown and
unpruned trees which can potentially be very large on some data sets. To
reduce memory consumption, the complexity and size of the trees should be
controlled by setting those parameter values.

The :meth:`predict` method operates using the :func:`numpy.argmax`
function on the outputs of :meth:`predict_proba`. This means that in
case the highest predicted probabilities are tied, the classifier will
predict the tied class with the lowest index in :term:`classes_`.

References
----------

.. [1] https://en.wikipedia.org/wiki/Decision_tree_learning

.. [2] L. Breiman, J. Friedman, R. Olshen, and C. Stone, "Classification
       and Regression Trees", Wadsworth, Belmont, CA, 1984.

.. [3] T. Hastie, R. Tibshirani and J. Friedman. "Elements of Statistical
       Learning", Springer, 2009.

.. [4] L. Breiman, and A. Cutler, "Random Forests",
       https://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm

Examples
--------
>>> from sklearn.datasets import load_iris
>>> from sklearn.model_selection import cross_val_score
>>> from sklearn.tree import DecisionTreeClassifier
>>> clf = DecisionTreeClassifier(random_state=0)
>>> iris = load_iris()
>>> cross_val_score(clf, iris.data, iris.target, cv=10)
...                             # doctest: +SKIP
...
array([ 1.     ,  0.93...,  0.86...,  0.93...,  0.93...,
        0.93...,  0.93...,  1.     ,  0.93...,  1.      ])
File:           ~/.pyenv/versions/3.10.13/lib/python3.10/site-packages/sklearn/tree/_classes.py
Type:           ABCMeta
Subclasses:     ExtraTreeClassifier

dt = DecisionTreeClassifier(
    criterion="entropy", min_samples_leaf=0.05, monotonic_cst=[-1]
)

dt.fit(df_train[["limit_bal"]], df_train["y"])

DecisionTreeClassifier(criterion='entropy', min_samples_leaf=0.05,
                       monotonic_cst=[-1])

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.

breaks = dt.tree_.threshold[dt.tree_.feature >= 0]

df_train.group_by(pl.col("limit_bal").cut(breaks)).agg(pl.col("y").mean()).pipe(
    px.line, x="limit_bal", y="y"
)

plt.figure(figsize=(20, 10))
_ = plot_tree(dt, feature_names=["limit_bal"], proportion=True, fontsize=8)

df.select(pl.col("limit_bal"))

shape: (30_000, 24)

limit_bal	sex	education	marriage	age	pay_0	pay_2	pay_3	pay_4	pay_5	pay_6	bill_amt1	bill_amt2	bill_amt3	bill_amt4	bill_amt5	bill_amt6	pay_amt1	pay_amt2	pay_amt3	pay_amt4	pay_amt5	pay_amt6	y
i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64	i64
20000	2	2	1	24	2	2	-1	-1	-2	-2	3913	3102	689	0	0	0	0	689	0	0	0	0	1
120000	2	2	2	26	-1	2	0	0	0	2	2682	1725	2682	3272	3455	3261	0	1000	1000	1000	0	2000	1
90000	2	2	2	34	0	0	0	0	0	0	29239	14027	13559	14331	14948	15549	1518	1500	1000	1000	1000	5000	0
50000	2	2	1	37	0	0	0	0	0	0	46990	48233	49291	28314	28959	29547	2000	2019	1200	1100	1069	1000	0
50000	1	2	1	57	-1	0	-1	0	0	0	8617	5670	35835	20940	19146	19131	2000	36681	10000	9000	689	679	0
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
220000	1	3	1	39	0	0	0	0	0	0	188948	192815	208365	88004	31237	15980	8500	20000	5003	3047	5000	1000	0
150000	1	3	2	43	-1	-1	-1	-1	0	0	1683	1828	3502	8979	5190	0	1837	3526	8998	129	0	0	0
30000	1	2	2	37	4	3	2	-1	0	0	3565	3356	2758	20878	20582	19357	0	0	22000	4200	2000	3100	1
80000	1	3	1	41	1	-1	0	0	0	-1	-1645	78379	76304	52774	11855	48944	85900	3409	1178	1926	52964	1804	1
50000	1	2	1	46	0	0	0	0	0	0	47929	48905	49764	36535	32428	15313	2078	1800	1430	1000	1000	1000	1

limit_bal